Statistical ranking with dynamic covariates
Fuente:
arXiv
Guardado en:
| Autores principales: | , , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866915205109252096 |
|---|---|
| author | Dong, Pinjun Han, Ruijian Jiang, Binyan Xu, Yiming |
| author_facet | Dong, Pinjun Han, Ruijian Jiang, Binyan Xu, Yiming |
| contents | We introduce a general covariate-assisted statistical ranking model within the Plackett--Luce framework. Unlike previous studies focusing on individual effects with fixed covariates, our model allows covariates to vary across comparisons. This added flexibility enhances model fitting yet brings significant challenges in analysis. This paper addresses these challenges in the context of maximum likelihood estimation (MLE). We first provide sufficient and necessary conditions for both model identifiability and the unique existence of the MLE. Then, we develop an efficient alternating maximization algorithm to compute the MLE. Under suitable assumptions on the design of comparison graphs and covariates, we establish a uniform consistency result for the MLE, with convergence rates determined by the asymptotic graph connectivity. We also construct random designs where the proposed assumptions hold almost surely. Numerical studies are conducted to support our findings and demonstrate the model's application to real-world datasets, including horse racing and tennis competitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_16507 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Statistical ranking with dynamic covariates Dong, Pinjun Han, Ruijian Jiang, Binyan Xu, Yiming Methodology Machine Learning We introduce a general covariate-assisted statistical ranking model within the Plackett--Luce framework. Unlike previous studies focusing on individual effects with fixed covariates, our model allows covariates to vary across comparisons. This added flexibility enhances model fitting yet brings significant challenges in analysis. This paper addresses these challenges in the context of maximum likelihood estimation (MLE). We first provide sufficient and necessary conditions for both model identifiability and the unique existence of the MLE. Then, we develop an efficient alternating maximization algorithm to compute the MLE. Under suitable assumptions on the design of comparison graphs and covariates, we establish a uniform consistency result for the MLE, with convergence rates determined by the asymptotic graph connectivity. We also construct random designs where the proposed assumptions hold almost surely. Numerical studies are conducted to support our findings and demonstrate the model's application to real-world datasets, including horse racing and tennis competitions. |
| title | Statistical ranking with dynamic covariates |
| topic | Methodology Machine Learning |
| url | https://arxiv.org/abs/2406.16507 |